Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
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![## Reaction Kinetics Study Across Different Temperatures
The kinetics of a certain reaction were studied at five different temperatures, with the rate constant measured at each temperature. As expected, the reaction rate (k) increases with temperature. The data is summarized in the table below:
| Temperature (°C) | 47.3 | 50.9 | 55.0 | 60.0 | 66.0 |
|------------------|-------|------|------|------|------|
| Rate Constant (k, 1/sec) | 0.263 | 0.354 | 0.606 | 1.022 | 1.873 |
To further analyze this data and calculate the activation energy (Eₐ) in kJ/mol for the reaction, we use the Arrhenius equation:
\[ k = A e^{-\frac{E_a}{RT}} \]
Where:
- \( k \) is the rate constant,
- \( A \) is the pre-exponential factor,
- \( E_a \) is the activation energy,
- \( R \) is the gas constant (8.314 J/mol·K),
- \( T \) is the absolute temperature in Kelvin (K).
### Steps to Calculate Activation Energy:
1. **Convert temperatures from Celsius to Kelvin** using the formula \( T(K) = T(°C) + 273.15 \).
2. **Apply the Arrhenius equation** by taking the natural logarithm of both sides, resulting in the linear form:
\[ \ln(k) = \ln(A) - \frac{E_a}{R}\left(\frac{1}{T}\right) \]
3. **Plot \(\ln(k)\) versus \(\frac{1}{T}\)**. The slope of the resulting line will be \(-\frac{E_a}{R}\).
Using this approach on the provided data will yield a straight line, from which the activation energy Eₐ can be calculated.](https://content.bartleby.com/qna-images/question/4f7442e5-ed1a-4154-ba5d-4813abad6cff/482a9769-b0d6-47d7-8f9e-157f75b8d9aa/rm5bgd.png)
Transcribed Image Text:## Reaction Kinetics Study Across Different Temperatures
The kinetics of a certain reaction were studied at five different temperatures, with the rate constant measured at each temperature. As expected, the reaction rate (k) increases with temperature. The data is summarized in the table below:
| Temperature (°C) | 47.3 | 50.9 | 55.0 | 60.0 | 66.0 |
|------------------|-------|------|------|------|------|
| Rate Constant (k, 1/sec) | 0.263 | 0.354 | 0.606 | 1.022 | 1.873 |
To further analyze this data and calculate the activation energy (Eₐ) in kJ/mol for the reaction, we use the Arrhenius equation:
\[ k = A e^{-\frac{E_a}{RT}} \]
Where:
- \( k \) is the rate constant,
- \( A \) is the pre-exponential factor,
- \( E_a \) is the activation energy,
- \( R \) is the gas constant (8.314 J/mol·K),
- \( T \) is the absolute temperature in Kelvin (K).
### Steps to Calculate Activation Energy:
1. **Convert temperatures from Celsius to Kelvin** using the formula \( T(K) = T(°C) + 273.15 \).
2. **Apply the Arrhenius equation** by taking the natural logarithm of both sides, resulting in the linear form:
\[ \ln(k) = \ln(A) - \frac{E_a}{R}\left(\frac{1}{T}\right) \]
3. **Plot \(\ln(k)\) versus \(\frac{1}{T}\)**. The slope of the resulting line will be \(-\frac{E_a}{R}\).
Using this approach on the provided data will yield a straight line, from which the activation energy Eₐ can be calculated.
![### Decomposition Reaction of Nickel Carbonyl
**Chemical Equation:**
\[ \text{Ni(CO)}_4(g) \rightarrow \text{Ni}(s) + 4 \text{CO}(g) \]
**Explanation:**
This chemical equation illustrates the decomposition reaction of nickel carbonyl.
- **Ni(CO)_4** represents nickel tetracarbonyl, a gaseous compound where a nickel (Ni) atom is bonded to four carbon monoxide (CO) molecules.
- The decomposition of nickel carbonyl results in the formation of solid nickel (Ni) and gaseous carbon monoxide (CO).
In this reaction:
- The nickel carbonyl (Ni(CO)_4) is a volatile complex that decomposes upon heating.
- The product on the left side of the equation shows nickel carbonyl in the gaseous state (g).
- The products on the right side of the equation include nickel in the solid state (s) and four molecules of carbon monoxide in the gaseous state (g).
This reaction is significant in industrial contexts, particularly in the purification of nickel via the Mond process, where impure nickel is reacted with carbon monoxide to form nickel tetracarbonyl, which then decomposes to yield pure nickel.](https://content.bartleby.com/qna-images/question/4f7442e5-ed1a-4154-ba5d-4813abad6cff/482a9769-b0d6-47d7-8f9e-157f75b8d9aa/kmdlwjj.png)
Transcribed Image Text:### Decomposition Reaction of Nickel Carbonyl
**Chemical Equation:**
\[ \text{Ni(CO)}_4(g) \rightarrow \text{Ni}(s) + 4 \text{CO}(g) \]
**Explanation:**
This chemical equation illustrates the decomposition reaction of nickel carbonyl.
- **Ni(CO)_4** represents nickel tetracarbonyl, a gaseous compound where a nickel (Ni) atom is bonded to four carbon monoxide (CO) molecules.
- The decomposition of nickel carbonyl results in the formation of solid nickel (Ni) and gaseous carbon monoxide (CO).
In this reaction:
- The nickel carbonyl (Ni(CO)_4) is a volatile complex that decomposes upon heating.
- The product on the left side of the equation shows nickel carbonyl in the gaseous state (g).
- The products on the right side of the equation include nickel in the solid state (s) and four molecules of carbon monoxide in the gaseous state (g).
This reaction is significant in industrial contexts, particularly in the purification of nickel via the Mond process, where impure nickel is reacted with carbon monoxide to form nickel tetracarbonyl, which then decomposes to yield pure nickel.
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